building block leading to trigonometry (ie. sine, cosine)
draw right angle triangles without a protractor
real world applications:
how long does the ladder need to be to reach the rooftop?
what is the length of the hill?
can i throw a 2 x 2 m sheet of plywood through a 1 x 1.5 m window diagonally?
build a bike ramp that will clear a 2 m fence
Why do we need to learn about multiplying and dividing with Integers?
Integers can be used to model money, buying and selling, and in particular debt - because most kids have allowances and some will be starting their first jobs. (Ex. If you owe $3 you can represent it as -3).
Integers are used in weather reports. (Ex. -3C, 5C, if it is -20C and temperature drops 3 degrees you end up at -23C).
Integers are used in sports statistics, (Ex. Hockey).
Integers are used in many online/video games (Ex. Halo point system).
Integers can be used to model cell phone text message limits. (Ex. You have 500 potential text messages for the year, if you use 10 a day when will you run out?).
Why do we need to learn about multiplying and dividing with Fractions?
Cooking and baking (Increasing or decreasing recipes)
In real life, we need to separate whole numbers into fractional objects (Ex. splitting a bill, dividing a cake, dividing homework assignments, etc)
Need for precision in measurement (Height, shoe sizes)
Music (Quarter notes, half notes)
Amount of free space remaining on an mp3 player
Test totals (If you get 3/4 on 3 questions and 4/4 on 2 questions, what is your total grade?)
Understanding sales ( 1/2 off our already reduced prices)
Why do we need to learn about calculating area and volume?
comparing volumes in order to save money (optimization)
optimize area to build ice rink in back yard
know how much paint is needed to paint your walls in your room
to know which cup is actually bigger to get more chocolate milk than your siblings
wrapping gifts
baking
building a house for habitat for humanity
Why do we need to learn about decimals and ratios?
money is based on decimals and ratios
calculating tax and sale prices
some recipes use ratios (e.g. rice cooks in a ratio of 1:2 with water)
maps use ratios (e.g. scales)
in sports - the statistics on players; co-ed male to female ratios
in art for spatial enlargement (like a photocopier does)
viewing size on computers (75%, 100%, 130%)
Why do we need to solve equations?
long term:
money problems (managing your own finances, including taxes)
baking (finding how much of each ingredient you need
buying things online (costs + S&H + taxes)
determining what mark you are striving for
determining costs for group activity, with coupons or discounts (i.e. a birthday party, school dance, graduation)
predicting winners (elections, sports, betting)
prediction of effects on the environment and what to expect for the future
History of Math
Check this set of videos out - it helps put math in perspective
Grade 8
Why do we need to learn about the Pythagorean Theorem?
Why do we need to learn about multiplying and dividing with Integers?
Why do we need to learn about multiplying and dividing with Fractions?
Why do we need to learn about calculating area and volume?
Why do we need to learn about decimals and ratios?
Why do we need to solve equations?